Nuprl Lemma : int_upper_subtype_int_upper

`∀[n,m:ℤ].  {n...} ⊆r {m...} supposing m ≤ n`

Proof

Definitions occuring in Statement :  int_upper: `{i...}` uimplies: `b supposing a` subtype_rel: `A ⊆r B` uall: `∀[x:A]. B[x]` le: `A ≤ B` int: `ℤ`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` int_upper: `{i...}` so_lambda: `λ2x.t[x]` so_apply: `x[s]` subtype_rel: `A ⊆r B` prop: `ℙ` all: `∀x:A. B[x]` implies: `P `` Q` le: `A ≤ B` and: `P ∧ Q` guard: `{T}`
Lemmas referenced :  subtype_rel_sets le_wf le_transitivity
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule lemma_by_obid sqequalHypSubstitution isectElimination thin intEquality because_Cache lambdaEquality hypothesisEquality hypothesis independent_isectElimination setElimination rename setEquality lambdaFormation productElimination axiomEquality isect_memberEquality equalityTransitivity equalitySymmetry

Latex:
\mforall{}[n,m:\mBbbZ{}].    \{n...\}  \msubseteq{}r  \{m...\}  supposing  m  \mleq{}  n

Date html generated: 2016_05_13-PM-03_33_03
Last ObjectModification: 2015_12_26-AM-09_44_54

Theory : arithmetic

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